Meditation is not without Orthodox precedent, though. Another "hot button" issue is the popular Stations of the Cross devotion and its use amongst Orthodox, which seems to center around this same concept of meditation somehow being improper. And then you read quotes like these and wonder what all the fuss is about.
Draw near all of you, children of the Church,
bought with the precious and holy blood of the most pure Master.
Come, let us meditate on his sufferings with tears,
thinking on fear, meditating with trembling,
saying to ourselves,
‘Christ our Saviour for us the impious was given over to death’.
Learn well, brother, what it is you hear:
God who is without sin,
Son of the Most High,
for you was given up.
Open your heart, learn in details His sufferings and say to yourself:
God who is without sin
today was given up,
today was mocked,
today was abused,
today was struck,
today was scourged,
today wore a crown of thorns,
today was crucified,
He, the heavenly Lamb.
Your heart will tremble, your soul will shudder.
Shed tears everyday by this meditation on the Master's sufferings.
Tears become sweet (for) the soul is enlightened that always meditates on Christ's sufferings.
Always meditating thus, shedding tears every day,
giving thanks to the Master for the sufferings that he suffered for you,
so that in the day of his Coming your tears may become your boast and exaltation before the judgment seat.
Endure as you meditate on the loving Master’s sufferings,
endure temptations, give thanks from your soul.
Blessed is the one who has before his eyes
the heavenly Master and his sufferings,
and has crucified himself from all the passions
and earthly deeds,
who has become an imitator
of his own Master.
-St. Ephraim the Syrian
Let us not merely read of these things, but bear them in our mind; the crown of thorns, the robe, the reed, the blows, the smiting on the cheek, the spittings, the irony. These things, if continually meditated on, are sufficient to take down all anger.
— St. John Chrysostom
Try to know yourself, your own wickedness. Think on the greatness of God and your wretchedness. Meditate on the suffering of Christ, the magnitude of Whose love and suffering surpass our understanding.
— St. Tikhon of Zadonsk
I'm not saying that any ol' thought that pops into our head should be dwelt upon, but there is definitely a means of pondering and meditating upon things such as the sufferings of Christ, that are acceptable within Orthodoxy. An Orthodox form of the Rosary, which can be found Lulu.com for a mere $5, is a very beautiful form of the devotion and any Orthodox Christian should have no worries about praying it if they want to.